Modeling a pointy mesh
Sharpen with Crease edges values

If is suitable with your geometry, you can use a high value of Crease Edge amount to the edges that start from the vertex you want pointy.

Pick the vertices, extend selection with Ctrl++ and than Ctrl+E to set the Crease to 1



More purple the edge is, higer the Crease value result.



If you are not interest on the sharp edges but only to create a spiky geometery, you can loopcut the piramid with a loopcut that lay in the plane that has the same normal of the base.



To opbtain this you can use the kinfe tool, or by extruding, or subdividing.

Double press G key to slide the loop near the vertex.